Solve Quadratic Equations Having Real Solutions by Factoring

Ethan, Michael, and Benjamin are on a treasure hunt. They come across a mysterious door with a riddle that reads, 'What is the first step in solving a quadratic equation by factoring?'

• Set the equation equal to zero.

• Factor the equation completely.

• Find the discriminant of the equation.

• Solve for the variable in the equation.

Answer explanation

The first step in solving a quadratic equation by factoring is to set the equation equal to zero.

What is the quadratic formula used for?

• To find the solutions or roots of a quadratic equation.

• To find the sum of two numbers.

• To calculate the area of a triangle.

• To determine the slope of a line.

Answer explanation

The quadratic formula is used to find the solutions or roots of a quadratic equation.

What is the process of factoring a quadratic equation?

• Factoring a quadratic equation involves finding the square root of the equation.

• Factoring a quadratic equation involves breaking it down into its factors.

• Factoring a quadratic equation involves multiplying the equation by its conjugate.

• Factoring a quadratic equation involves rearranging the terms of the equation.

Answer explanation

Factoring a quadratic equation involves breaking it down into its factors.

Abigail, Lily, and Kai are having a friendly debate. They are trying to figure out how many solutions a quadratic equation can have. Can you help them settle this?

• 2

• 3

• 1

• 0

Answer explanation

A quadratic equation can have two solutions.

Solve the equation by factoring.

• x = {3,8}

• x = {-3,8}

• x = {3,-8}

• x = {-3,-8}

Solve by factoring. (HINT: Factor GCF 1st)

• x = 3, x = -6

• x = 0, x = 2

• x = 2, x = 3

• x = -2, x = 1

Solve for x by factoring.

• -6, -2

• -2, 6

• 2, 6

• -6, 2

Solve by factoring

• -4, 2

• -2, 4

• -16

• -4

Solve for k by factoring.

• A

• B

• C

• D

Solve this quadratic.

• {-4, 2}

• {-2, 4}

• {-16}

• {-4}